If alfa and bita are the …
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Sia ? 6 years, 3 months ago
We have, α and β are the roots of the quadratic polynomial. f(x) =x2 - 5x + 4
Sum of zeros: {tex}\alpha+\beta=-\frac{b}{a}=-\frac{\text { coefficient of } x}{\text { coefficient of } x^{2}}{/tex}
product of zeros: {tex}\alpha \beta=\frac{c}{a}=\frac{\text { constant term }}{\text { coefficient of } x^{2}}{/tex}
We have a=1,b=-5 and c= 4.
Sum of the roots = α + β = 5
Product of the roots = αβ = 4
So,
{tex}\frac{1}{\alpha } + \frac{1}{\beta } - 2\alpha \beta = \frac{{\beta + \alpha }}{{\alpha \beta }} - 2\alpha \beta{/tex}
{tex}5/4-2\times4=5/4-8{/tex} ={tex}\left(5-32\right)/4{/tex}={tex}-27/4{/tex}
Hence,we get the result of {tex}\frac{{ 1 }}{\alpha} + \frac{{ 1 }}{\beta} - 2\alpha\beta{/tex} = {tex}-\frac{{ 27 }}{ 4}{/tex}
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